Determining the interset distance
Abstract The following problem is considered. We are given a vector space that can be the vector space $$\mathbb {R}^m$$ or the vector space of symmetric $$m \times m$$ matrices $$\mathbb {S}^m.$$ There are two sets of vectors $$\{a_i, 1 \le i \le r\}$$ and $$\{b_j, 1 \le j \le q\}$$ in that vector...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Barketau, Maksim [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, LLC, part of Springer Nature 2019 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of combinatorial optimization - Springer US, 1997, 38(2019), 1 vom: 25. Jan., Seite 316-332 |
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| Übergeordnetes Werk: |
volume:38 ; year:2019 ; number:1 ; day:25 ; month:01 ; pages:316-332 |
| Links: |
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| DOI / URN: |
10.1007/s10878-019-00384-3 |
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OLC2044625229 |
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| 520 | |a Abstract The following problem is considered. We are given a vector space that can be the vector space $$\mathbb {R}^m$$ or the vector space of symmetric $$m \times m$$ matrices $$\mathbb {S}^m.$$ There are two sets of vectors $$\{a_i, 1 \le i \le r\}$$ and $$\{b_j, 1 \le j \le q\}$$ in that vector space. Let K be some convex cone in the corresponding space. Let $$a_i \ge _K b_j, \forall i,j,$$ where $$a_i \ge _K b_j$$ mean that $$a_i-b_j \in K.$$ Let $$\mathcal {A}_{\le }=\{x | a_i \ge _K x, \forall i, 1 \le i \le r \},$$ where $$a_i \ge _K x$$ mean that $$a_i-x \in K.$$ Further let $$\mathcal {B}_{\ge }=\{y | y \ge _K b_j, \forall j, 1 \le j \le q \}.$$ In this work we study the question of finding and upperbounding the distance from the set $$\mathcal {A}_{\le }$$ to the set $$\mathcal {B}_{\ge }$$ in the case of cones $$\mathbb {R}_+^m, \mathbb {L}^m, \mathbb {S}_+^m$$. | ||
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10.1007/s10878-019-00384-3 doi (DE-627)OLC2044625229 (DE-He213)s10878-019-00384-3-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn Barketau, Maksim verfasserin aut Determining the interset distance 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract The following problem is considered. We are given a vector space that can be the vector space $$\mathbb {R}^m$$ or the vector space of symmetric $$m \times m$$ matrices $$\mathbb {S}^m.$$ There are two sets of vectors $$\{a_i, 1 \le i \le r\}$$ and $$\{b_j, 1 \le j \le q\}$$ in that vector space. Let K be some convex cone in the corresponding space. Let $$a_i \ge _K b_j, \forall i,j,$$ where $$a_i \ge _K b_j$$ mean that $$a_i-b_j \in K.$$ Let $$\mathcal {A}_{\le }=\{x | a_i \ge _K x, \forall i, 1 \le i \le r \},$$ where $$a_i \ge _K x$$ mean that $$a_i-x \in K.$$ Further let $$\mathcal {B}_{\ge }=\{y | y \ge _K b_j, \forall j, 1 \le j \le q \}.$$ In this work we study the question of finding and upperbounding the distance from the set $$\mathcal {A}_{\le }$$ to the set $$\mathcal {B}_{\ge }$$ in the case of cones $$\mathbb {R}_+^m, \mathbb {L}^m, \mathbb {S}_+^m$$. Conic optimization Quadratic optimization Semidefinite optimization Enthalten in Journal of combinatorial optimization Springer US, 1997 38(2019), 1 vom: 25. Jan., Seite 316-332 (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:38 year:2019 number:1 day:25 month:01 pages:316-332 https://doi.org/10.1007/s10878-019-00384-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2108 AR 38 2019 1 25 01 316-332 |
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10.1007/s10878-019-00384-3 doi (DE-627)OLC2044625229 (DE-He213)s10878-019-00384-3-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn Barketau, Maksim verfasserin aut Determining the interset distance 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract The following problem is considered. We are given a vector space that can be the vector space $$\mathbb {R}^m$$ or the vector space of symmetric $$m \times m$$ matrices $$\mathbb {S}^m.$$ There are two sets of vectors $$\{a_i, 1 \le i \le r\}$$ and $$\{b_j, 1 \le j \le q\}$$ in that vector space. Let K be some convex cone in the corresponding space. Let $$a_i \ge _K b_j, \forall i,j,$$ where $$a_i \ge _K b_j$$ mean that $$a_i-b_j \in K.$$ Let $$\mathcal {A}_{\le }=\{x | a_i \ge _K x, \forall i, 1 \le i \le r \},$$ where $$a_i \ge _K x$$ mean that $$a_i-x \in K.$$ Further let $$\mathcal {B}_{\ge }=\{y | y \ge _K b_j, \forall j, 1 \le j \le q \}.$$ In this work we study the question of finding and upperbounding the distance from the set $$\mathcal {A}_{\le }$$ to the set $$\mathcal {B}_{\ge }$$ in the case of cones $$\mathbb {R}_+^m, \mathbb {L}^m, \mathbb {S}_+^m$$. Conic optimization Quadratic optimization Semidefinite optimization Enthalten in Journal of combinatorial optimization Springer US, 1997 38(2019), 1 vom: 25. Jan., Seite 316-332 (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:38 year:2019 number:1 day:25 month:01 pages:316-332 https://doi.org/10.1007/s10878-019-00384-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2108 AR 38 2019 1 25 01 316-332 |
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10.1007/s10878-019-00384-3 doi (DE-627)OLC2044625229 (DE-He213)s10878-019-00384-3-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn Barketau, Maksim verfasserin aut Determining the interset distance 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract The following problem is considered. We are given a vector space that can be the vector space $$\mathbb {R}^m$$ or the vector space of symmetric $$m \times m$$ matrices $$\mathbb {S}^m.$$ There are two sets of vectors $$\{a_i, 1 \le i \le r\}$$ and $$\{b_j, 1 \le j \le q\}$$ in that vector space. Let K be some convex cone in the corresponding space. Let $$a_i \ge _K b_j, \forall i,j,$$ where $$a_i \ge _K b_j$$ mean that $$a_i-b_j \in K.$$ Let $$\mathcal {A}_{\le }=\{x | a_i \ge _K x, \forall i, 1 \le i \le r \},$$ where $$a_i \ge _K x$$ mean that $$a_i-x \in K.$$ Further let $$\mathcal {B}_{\ge }=\{y | y \ge _K b_j, \forall j, 1 \le j \le q \}.$$ In this work we study the question of finding and upperbounding the distance from the set $$\mathcal {A}_{\le }$$ to the set $$\mathcal {B}_{\ge }$$ in the case of cones $$\mathbb {R}_+^m, \mathbb {L}^m, \mathbb {S}_+^m$$. Conic optimization Quadratic optimization Semidefinite optimization Enthalten in Journal of combinatorial optimization Springer US, 1997 38(2019), 1 vom: 25. Jan., Seite 316-332 (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:38 year:2019 number:1 day:25 month:01 pages:316-332 https://doi.org/10.1007/s10878-019-00384-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2108 AR 38 2019 1 25 01 316-332 |
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10.1007/s10878-019-00384-3 doi (DE-627)OLC2044625229 (DE-He213)s10878-019-00384-3-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn Barketau, Maksim verfasserin aut Determining the interset distance 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract The following problem is considered. We are given a vector space that can be the vector space $$\mathbb {R}^m$$ or the vector space of symmetric $$m \times m$$ matrices $$\mathbb {S}^m.$$ There are two sets of vectors $$\{a_i, 1 \le i \le r\}$$ and $$\{b_j, 1 \le j \le q\}$$ in that vector space. Let K be some convex cone in the corresponding space. Let $$a_i \ge _K b_j, \forall i,j,$$ where $$a_i \ge _K b_j$$ mean that $$a_i-b_j \in K.$$ Let $$\mathcal {A}_{\le }=\{x | a_i \ge _K x, \forall i, 1 \le i \le r \},$$ where $$a_i \ge _K x$$ mean that $$a_i-x \in K.$$ Further let $$\mathcal {B}_{\ge }=\{y | y \ge _K b_j, \forall j, 1 \le j \le q \}.$$ In this work we study the question of finding and upperbounding the distance from the set $$\mathcal {A}_{\le }$$ to the set $$\mathcal {B}_{\ge }$$ in the case of cones $$\mathbb {R}_+^m, \mathbb {L}^m, \mathbb {S}_+^m$$. Conic optimization Quadratic optimization Semidefinite optimization Enthalten in Journal of combinatorial optimization Springer US, 1997 38(2019), 1 vom: 25. Jan., Seite 316-332 (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:38 year:2019 number:1 day:25 month:01 pages:316-332 https://doi.org/10.1007/s10878-019-00384-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2108 AR 38 2019 1 25 01 316-332 |
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Abstract The following problem is considered. We are given a vector space that can be the vector space $$\mathbb {R}^m$$ or the vector space of symmetric $$m \times m$$ matrices $$\mathbb {S}^m.$$ There are two sets of vectors $$\{a_i, 1 \le i \le r\}$$ and $$\{b_j, 1 \le j \le q\}$$ in that vector space. Let K be some convex cone in the corresponding space. Let $$a_i \ge _K b_j, \forall i,j,$$ where $$a_i \ge _K b_j$$ mean that $$a_i-b_j \in K.$$ Let $$\mathcal {A}_{\le }=\{x | a_i \ge _K x, \forall i, 1 \le i \le r \},$$ where $$a_i \ge _K x$$ mean that $$a_i-x \in K.$$ Further let $$\mathcal {B}_{\ge }=\{y | y \ge _K b_j, \forall j, 1 \le j \le q \}.$$ In this work we study the question of finding and upperbounding the distance from the set $$\mathcal {A}_{\le }$$ to the set $$\mathcal {B}_{\ge }$$ in the case of cones $$\mathbb {R}_+^m, \mathbb {L}^m, \mathbb {S}_+^m$$. © Springer Science+Business Media, LLC, part of Springer Nature 2019 |
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Abstract The following problem is considered. We are given a vector space that can be the vector space $$\mathbb {R}^m$$ or the vector space of symmetric $$m \times m$$ matrices $$\mathbb {S}^m.$$ There are two sets of vectors $$\{a_i, 1 \le i \le r\}$$ and $$\{b_j, 1 \le j \le q\}$$ in that vector space. Let K be some convex cone in the corresponding space. Let $$a_i \ge _K b_j, \forall i,j,$$ where $$a_i \ge _K b_j$$ mean that $$a_i-b_j \in K.$$ Let $$\mathcal {A}_{\le }=\{x | a_i \ge _K x, \forall i, 1 \le i \le r \},$$ where $$a_i \ge _K x$$ mean that $$a_i-x \in K.$$ Further let $$\mathcal {B}_{\ge }=\{y | y \ge _K b_j, \forall j, 1 \le j \le q \}.$$ In this work we study the question of finding and upperbounding the distance from the set $$\mathcal {A}_{\le }$$ to the set $$\mathcal {B}_{\ge }$$ in the case of cones $$\mathbb {R}_+^m, \mathbb {L}^m, \mathbb {S}_+^m$$. © Springer Science+Business Media, LLC, part of Springer Nature 2019 |
| abstract_unstemmed |
Abstract The following problem is considered. We are given a vector space that can be the vector space $$\mathbb {R}^m$$ or the vector space of symmetric $$m \times m$$ matrices $$\mathbb {S}^m.$$ There are two sets of vectors $$\{a_i, 1 \le i \le r\}$$ and $$\{b_j, 1 \le j \le q\}$$ in that vector space. Let K be some convex cone in the corresponding space. Let $$a_i \ge _K b_j, \forall i,j,$$ where $$a_i \ge _K b_j$$ mean that $$a_i-b_j \in K.$$ Let $$\mathcal {A}_{\le }=\{x | a_i \ge _K x, \forall i, 1 \le i \le r \},$$ where $$a_i \ge _K x$$ mean that $$a_i-x \in K.$$ Further let $$\mathcal {B}_{\ge }=\{y | y \ge _K b_j, \forall j, 1 \le j \le q \}.$$ In this work we study the question of finding and upperbounding the distance from the set $$\mathcal {A}_{\le }$$ to the set $$\mathcal {B}_{\ge }$$ in the case of cones $$\mathbb {R}_+^m, \mathbb {L}^m, \mathbb {S}_+^m$$. © Springer Science+Business Media, LLC, part of Springer Nature 2019 |
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Determining the interset distance |
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